# Chapter 10 :Kinetic Theory of Gases¶

## Example 10.4 , Page no:58¶

In [1]:
import math
from __future__ import division

#initialisation of variables
gp=200; #gauge pressure in lb/in square
atmp=15; #atmospheric pressure in lb/in square
v1=3; #volume in ft cube
p2=15; #pressure at sea-level in lb/in square

#CALCULATIONS
p1=gp+atmp; #pressure in lb/in square
v2=(p1*v1)/p2; #calculating pressure in ft cube using Boyle's law  ie. p1*v1=p2*v2 at constant temperature

#RESULTS
print"Volume occupied in ft cube =",round(v2,3);

Volume occupied in ft cube = 43.0


## Example 10.5 , Page no:58¶

In [2]:
import math
from __future__ import division

#initialisation of variables
p1=300+15; #absolute pressure in lb/in square
p2=15; #pressure in lb/in square
v1=3; #volume in ft cube

#CALCULATIONS
v2=(p1*v1)/p2; #calculating v2 using Boyle's law at const. temp.
v3=v2-43;

#RESULTS
print"Volume in ft cube =",round(v2,3);
print"Additional Volume of air in ft cube =",round(v3,3);

Volume in ft cube = 63.0
Additional Volume of air in ft cube = 20.0


## Example 10.6 , Page no:59¶

In [3]:
import math
from __future__ import division

#initialisation of variables
Tc=-196; #Boiling Point of Nitrogen in celcius

#CALCULATIONS
Tk=Tc+273; #calculating B.P. in Kelvin using Kelvin=Celcius+273

#RESULTS
print"Boiling Point of Nitrogen in Kelvin =",round(Tk,3);

Boiling Point of Nitrogen in Kelvin = 77.0


## Example 10.7 , Page no:59¶

In [4]:
import math
from __future__ import division

#initialisation of variables
tk=6000; #temperature in Kelvin

#CALCULATIONS
tk1=tk-273;

#RESULTS
print"Temperature in celcius =",round(tk1,3);

Temperature in celcius = 5727.0


## Example 10.8 , Page no:59¶

In [5]:
import math
from __future__ import division

#initialisation of variables
t1=273; #temperature in Kelvin
v2=2; #twice v1

#CALCULATIONS
t3=(t1*v2)-273;

#RESULTS
print"Temperature in celcius =",round(t3,3);

Temperature in celcius = 273.0


## Example 10.9 , Page no:59¶

In [6]:
import math
from __future__ import division

#initialisation of variables
T1=283; #temperature Kelvin
T2=322; #temp. in Kelvin
p1=35; #pressure in lb/in square

#CALCULATIONS
p2=(T2*p1)/T1; #calculating p2 using ideal gas equation since,v1=v2

#RESULTS
print"Pressure in lb/in square =",round(p2,3);

Pressure in lb/in square = 39.823


## Example 10.10 , Page no:59¶

In [7]:
import math
from __future__ import division

#initialisation of variables
t1=293; #temp in Kelvin
t2=233; #temp in Kelvin
v1=0.1; #volume in m cube
p1=10; #pressure in atm
p2=1; #pressure in atm
p3=1; #pressure in atm

#CALCULATIONS
v2=(p1*v1*t2)/(t1*p2);  #calculating v2 using ideal gas law
v3=(p1*v1)/p3; #calculating volume using ideal gas law
v4=v2-0.1;
v5=v3-0.1;

#RESULTS
print"(a)Volume of ballon in m cube =",round(v4,3);
print"(b)Volume of ballon after Helium absorbs heat from air  in m cube =",round(v5,3);

(a)Volume of ballon in m cube = 0.695
(b)Volume of ballon after Helium absorbs heat from air  in m cube = 0.9


## Example 10.11 , Page no:60¶

In [8]:
import math
from __future__ import division

#initialisation of variables
d1=1.293; #density in kg/m cube
t1=273; #temperature in Kelvin
p2=2; #pressure in atm
t2=373; #temperature in Kelvin
p1=1; #pressure in atm

#CALCULATIONS
d2=(d1*t1*p2)/(t2*p1); #calculating density using ideal gas law in kg/m cube

#RESULTS
print"Density in kg/m cube =",round(d2,3);

Density in kg/m cube = 1.893


## Example 10.12 , Page no:60¶

In [9]:
import math
from __future__ import division

#initialisation of variables
o=16.00; #atomic mass of O
h=1.008; #atomic mass of H
c=12.01; #atomic mass of carbon

#CALCULATIONS
mh2o=(o+2*h)*1.66*10**-27; #mass of H2O molecule
m=((2*c)+o+(6*h))*1.66*10**-27;  #mass of C2H6O molecule

#RESULTS
print"Mass of H20 molecule in kg =",'%.3E'%mh2o;
print"Mass of Ethyl Alcohol molecule in kg =",'%.3E'%m;

Mass of H20 molecule in kg = 2.991E-26
Mass of Ethyl Alcohol molecule in kg = 7.647E-26


## Example 10.13 , Page no:60¶

In [10]:
import math
from __future__ import division

#initialisation of variables
m=1; #mass of H2O in kg
m1=2.99*10**-26; #mass of H2O molecule in kg

#CALCULATIONS
mo=m/m1; #calculating no. of molecules of H2O using no=mass of H2O/mass of H2) molecule

#RESULTS
print"Molecules of H2O =",'%.3E'%mo;

Molecules of H2O = 3.344E+25


## Example 10.14 , Page no:60¶

In [11]:
import math
from __future__ import division

#initialisation of variables
k=1.38*10**-23; #Boltzmann's constant in J/K
tk=273+100; #absolute temp (in Kelvin)

#CALCULATIONS
KE=3/2*(k*tk); #calculating average Kinetic Energy in Joule using kinetic theory of gases

#RESULTS
print"Average Kinetic Energy in Joule =",'%.3E'%KE;

Average Kinetic Energy in Joule = 7.721E-21


## Example 10.15 , Page no:60¶

In [12]:
import math
from __future__ import division

#initialisation of variables
k=1.38*10**-23; #Boltzmann's constant in J/K
t=100+273; #temperature in Kelvin
m=5.3*10**-26; #mass of oxygen molecule in kg

#CALCULATIONS
v=math.sqrt((3*k*t)/m); #calculating average velocity using kinetic theory of gases.

#RESULTS
print"Average velocity of molecules in m/sec =",round(v,3);

Average velocity of molecules in m/sec = 539.78